Given the function f(x)=-(5)/(6)x^(2)+(1)/(5), then what is f(2x) as a simplified polynomial? Answer:

Substitute x in f(x): Substitute 2x into the function f(x). We need to replace every instance of x in the function with 2x. f(2x) = -(5/6)(2x)^2 + (1/5)Simplify square of (2x): Simplify the square of (2x). We need to square the term (2x) to get (2x)^2. (2x)^2 = (2^2)(x^2) = 4x^2Substitute squared term: Substitute the squared term back into the function. Now we replace (2x)^2 with 4x^2 in the function. f(2x) = -(5/6)(4x^2) + (1/5)Multiply coefficients: Multiply the coefficients. We need to multiply the coefficient -(5/6) by 4. -(5/6) * 4 = -20/6 = -10/3Write simplified polynomial: Write the simplified polynomial. Now we have the coefficient for x^2, we can write the simplified polynomial. f(2x) = -10/3x^2 + (1/5)

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Given the function
f(x)=-(5)/(6)x^(2)+(1)/(5), then what is
f(2x) as a simplified polynomial?
Answer:

Given the function $f(x)=-\frac{5}{6} x^{2}+\frac{1}{5}$ , then what is $f(2 x)$ as a simplified polynomial? $\newline$ Answer:

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Algebra 1

Multiplication with rational exponents

Full solution

Q. Given the function

f(x)=-\frac{5}{6} x^{2}+\frac{1}{5}

, then what is

f(2 x)

as a simplified polynomial?

\newline

Answer:

Substitute $x$ in $f(x)$ : Substitute $2x$ into the function $f(x)$ . We need to replace every instance of $x$ in the function with $2x$ . $f(2x) = -(\frac{5}{6})(2x)^2 + (\frac{1}{5})$
Simplify square of $(2x)$ : Simplify the square of $(2x)$ . We need to square the term $(2x)$ to get $(2x)^2$ . $(2x)^2 = (2^2)(x^2) = 4x^2$
Substitute squared term: Substitute the squared term back into the function. $\newline$ Now we replace $(2x)^2$ with $4x^2$ in the function. $\newline$ $f(2x) = -\left(\frac{5}{6}\right)(4x^2) + \left(\frac{1}{5}\right)$
Multiply coefficients: Multiply the coefficients. $\newline$ We need to multiply the coefficient $-\frac{5}{6}$ by $4$ . $\newline$ $-\frac{5}{6} \times 4 = -\frac{20}{6} = -\frac{10}{3}$
Write simplified polynomial: Write the simplified polynomial. $\newline$ Now we have the coefficient for $x^2$ , we can write the simplified polynomial. $\newline$ $f(2x) = -\frac{10}{3}x^2 + \left(\frac{1}{5}\right)$